Question

Evaluate arctan(-squareroot(3)/3) for an exact radian value in terms of pi.

Answer 1

what do you know about arctan(-x) ?

Answer 2

What i wrote was all that was given. From what i've understood so far it's in Q1.

Answer 3

Yes, the reason I asked what arctan(-x) equals to is because you need to use the identity to evaluate the given expression

Answer 4

It equals the angle of theta, no?

Answer 5

so arctan(-x) = x?

Answer 6

yes

Answer 7

or... wouldnt arctan(-x) equal tan(x)?

Answer 8

no, arctan(-x) = -arctan(x). This is the identity that will help you evaluate. So using the identity, what does the expression now equal to?

Answer 9

-arctan(squareroot(3)/3)...?

Answer 10

good.

so if you let Θ = arctan(sqrt(3) / 3), what does this equivalent to?

Answer 11

and that's where you lose me.

Answer 12

well, it's equivalent to tan(Θ) = sqrt(3)/3

Answer 13

gotcha

Answer 14

so 30 degrees since it's a 30 60 90 triangle, then convert to radians?

Answer 15

so what angle whose tangent is sqrt(3)/3 ?

Answer 16

which would be pi over 6?

Answer 17

excellent. But remember that you also have a negative sign in the front

Answer 18

so 330 degrees convert to radians, or negative pi over 6?

Answer 19

yep

Answer 20

so are negative pi over 6 and 11pi over 6 both valid answers? and thank you, you're a lifesaver

Answer 21

no, just pi/6.

Answer 22

i mean just -pi/6

Answer 23

gotcha. thank you again.